4.2 Angle Relationships in Triangles

dia/practice_quizzes/geo/geo_pq_trc_01.html dia/practice_quizzes/geo/geo_pq_trc_01.html

Goals for today! Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior angles of triangles.

Exploration Materials: Notecard, ruler, and scissors

Theorem/Postulate Page

Example 1 mXYZ + mYZX + mZXY = 180° mXYZ = 180 mXYZ = 180 mXYZ = 78° 2. Find m  YWZ. 1. Find m  XYZ mYXZ + mWXY = 180° 62 + mWXY = 180 mWXY = 118°

A corollary is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem.

Theorem/Postulate Page

Example 2 The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle? HINT: DRAW A PICTURE m  A + m  B = 90° m  B = 90 m  B = 26.3°

Interior and Exterior

Remote Interior Angles The remote interior angles of  4 are  1 and  2.

Theorem/Postulate Page

Example 3 Find m  B. m  A + m  B = m  BCD x + 3 = 5x – 60 2x + 18 = 5x – = 3x 26 = x m  B = 2x + 3 = 2(26) + 3 = 55°

Example 4 Find m  ACD. m  ACD = m  A + m  B 6z – 9 = 2z z – 9 = 2z z = 100 z = 25 m  ACD = 6z – 9 = 6(25) – 9 = 141°

Theorem/Postulate Page

Example 5 Find m  P and m  T. P  TP  T 2x 2 = 4x 2 – 32 –2x 2 = –32 x 2 = 16 So m  P = 2x 2 = 2(16) = 32°. Since m  P = m  T, m  T = 32°.

CHECK UP 1.The measure of one of the acute angles in a right triangle is 56°. What is the measure of the other acute angle? 2. Find m  ABD. 3. Find m  N and m  P.

Check Up 4. The diagram is a map showing John's house, Kay's house, and the grocery store. What is the angle the two houses make with the store?

Assignment Page all